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Abstract— Estimations of coherence bandwidth from wideband
channel sounding measurements made in the 30KHz–100MHz band in
several indoor environments are described. Results are intended for
applications in high-capacity indoor powerline networks. The
coherence bandwidth and the RMS delay spread parameters are
esti-mated from measurements of the complex transfer function of
the Powerline Com-munications (PLC) channel. The 90th percentile of
the estimated coherence band-width at 0.9 correlation level is
above 65.5 KHz and 90% of estimated values of B0.9 are below 691.5
KHz. B0.9 was observed to have a minimum value of 32.5 KHz. The RMS
delay spread describes the dispersion in the time domain due to
multipath transmission. 80 % of the channels exhibit an RMS delay
spread between 0.06μs and 0.78μs. Its mean value was equal to
0.413μs. The paper studies the variability of the coherence
bandwidth and time-delay spread parameters with the channel class
[9], and thus with the location of the receiver with respect to the
transmitter. And finally relates the RMS delay spread to the
coherence bandwidth, which in turn, affects the powerline channel
capacity.
Keywords— Powerline Communications (PLC), Coherence bandwidth,
RMS delay
spread.
– Introduction owerline Communications (PLC) appointed for
future wideband wireline
services in the 2-30 MHz frequency band envisage data
transmission rates up to 200 Mbits/s [1]. Generally, Effective data
rates do not exceed 70 Mbits/s [2]. In order to increase much more
the data rates, the PLC equipment suppliers are studying the
possibility of extending the PLC frequency band up to 100 MHz. The
successful implementation of this solution requires a detailed
knowledge of signal propagation modes inside this enlarged
band.
Coherence Bandwidth and its Relationship with the RMS delay
spread for PLC channels
using Measurements up to 100 MHz Mohamed Tlich1, Gautier Avril2,
Ahmed Zeddam2
1Teamlog, 2France Télécom division R&D 2, Av. Pierre Marzin
– 22303 Lannion, France
[email protected]
P
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2
Extensive characterizations of powerline channels have been
reported in [5, 6, 7, and 8]. However, these studies are mainly
focused on frequencies up to 30 MHz.
The coherence bandwidth is a key parameter whose value relative
to the band-width of the transmitted signal, subsequently
determines the need for employing channel protection techniques,
e.g. equalisation or coding to overcome the disper-sive effects of
multipath [3, 4]. The impulse response of transmission channels can
be characterised by various parameters. The average delay is
derived from the first moment of the delay power spectrum and is a
measure of the mean delay of sig-nals. The RMS delay spread is
derived from the second moment of the delay power spectrum and
describes the dispersion in the time domain due to multipath
transmission.
For PLC channels, and for the 1-30 MHz frequency band, thorough
studies were undertaken in [5, 6]. It was observed that 99% of the
studied channels have an RMS delay spread below 0.5μs. In [5], B0.9
was observed to have an average value of 1 MHz.
Also, in [7], it was indicated that for signals in the 0.5-15
MHz frequency band, the maximum excess delay was below 3μs, and the
minimum estimated value of B0.9 was 25 KHz.
In [8] and for the frequency range up to 30 MHz, it has been
found that, for 95 % of the channels the mean-delay spread is
between 160ns and 3.2μs. And 95 % of the channels exhibit an RMS
delay spread between 240ns and 2.5μs.
In this paper, coherence bandwidth and delay spread parameters
studies are ex-tended until the 100 MHz frequency band. For this
purpose wideband propagation measurements were undertaken in the 30
KHz – 100 MHz band in various indoor channel environments (country
and urban, new and old, apartments and houses) as demonstrated
Table 1.
The measurements taken using a swept frequency channel sounder
yielded suf-ficient statistical data from which frequency
correlation functions were derived. These results were used to
obtain the coherence bandwidth of the PLC channels investigated and
their impulse responses, obtained by applying the inverse Fourier
transform to the estimated frequency response [4].
The PLC transfer functions study presented hereby relates to
seven measure-ment sites and a total of 144 transfer functions. For
each site, the transfer function is measured between a principal
outlet (most probable to receive a PLC module) and the whole other
outlets (except improbable outlets such as refrigerator
out-lets...). The distribution of the transfer functions by site
and the characteristics of each site are given in the table 1.
TABLE 1 DISTRIBUTION OF TRANSFER FUNCTIONS BY SITE
Site number
Site information Number of transfer functions
1 House - Urban 19 2 New house - Urban 13
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3
3 Recently restored apartment – Ur-ban
12
4 Recent house – Urban 28 5 Recent house – Urban 34 6 Recent
house – country 22 7 Old House - country 16
Because calculating distances separating transmitters from
receivers was im-
possible, the PLC channels were classified into 9 classes per
ascending order of their capacities (according to the Shannon's
capacity formula and for a same refer-ence noise and PSD emission
mask). In [9] and as shows Fig.1, we have demon-strated that the
channels of each class had a transfer functions with a same average
magnitude.
Fig. 1. Average transfer function magnitude by class.
Thus, a class 9 channel will, for example, be supposed to have a
shorter trans-
mitter-receiver distance than a class 2-8 channel, and so
on.
– Channel Sounder Hardware This section outlines the swept
frequency channel sounder design, its calibra-
tion and the devices used in the measurements. Transfer function
measurements were carried out in the frequency domain, by means of
a vectorial network ana-lyser, as show the block diagram of the
Fig. 2.
The coupler box plugging into the AC wall outlet behaves like a
high-pass fil-ter, with the 3 dB cutoff at 30 KHz. The probing
signal passes through the coupler
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4
and the AC power line network and exits through a similar
coupler plugged in a different outlet. A direct coupler to coupler
connection is used to calibrate the test setup.
Fig. 2. Power line channel measurement system.
Two over-voltage limiting devices with a -10 dB and -6 dB
losses, respectively, are used in front of the entry port of the
vectorial network analyser 8753ES and its exit port, which can
serve as an entry port, to protect it from over-voltages pro-duced
by the impulse noises of the AC power line.
A computer is connected to the network analyzer through a GPIB
bus. This al-lows it to record data and control the network
analyser by the INTUILINK soft-ware.
The network analyzer and the computer are isolated from the
Powerline net-work using a filtered extension. This extension is
systematically connected to an outlet nonlikely to be connected to
a PLC modem, such as washing machine out-let. These precautions are
taken in order to minimize the influence of the meas-urement
devices on the measured transfer functions.
– Wideband Propagation Parameters Characterisation of wideband
channel performance subject to multipath can be
usefully described using the coherence bandwidth and delay
spread parameters.
Coherence Bandwidth The frequency-selective behaviour of the
channel can be described in terms of
the auto-correlation function for a wide sense stationary
uncorrelated scattering (WSSUS) channel. Equation (1) gives ( )R fΔ
, the frequency correlation function (FCF):
*( ) ( ) ( )R f H f H f f df+∞
−∞
Δ = + Δ∫ (1)
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5
Where ( )H f is the complex transfer function of the channel, fΔ
is the fre-
quency shift and * denotes the complex conjugate. ( )R fΔ is a
measure of the magnitude of correlation between the channel
response at two spaced frequencies. The coherence bandwidth is a
statistical measure of the range of frequencies over which the FCF
can be considered 'flat' (i.e. a channel passes all spectral
compo-nents with approximately equal gain and linear phase).
In other words, coherence bandwidth is the range of frequencies
over which two frequency components have a strong potential for
amplitude correlation. It is a frequency-domain parameter that is
useful for assessing the performances of vari-ous modulation
techniques [10]. No single definitive value of correlation has
emerged for the specification of coherence bandwidth. Hence,
coherence band-widths for generally accepted values of correlations
coefficient equal to 0.5, 0.7 and 0.9 were evaluated from each FCF,
and these are referred to as B0.5, B0.7 and B0.9, respectively.
RMS Delay Spread Random and complicated PLC propagation channels
can be characterized using
the impulse response approach. Here, the channel is a linear
filter with impulse re-sponse ( )h t . The power-delay profile
provides an indication of the dispersion or distribution of
transmitted power over various paths in a multipath model for
propagation. The power-delay profile of the channel is calculated
by taking the spatial average of 2( )h t . It can be thought of as
a density function, of the form:
2
2
( )( )
( )
h tP
h t dt
τ+∞
−∞
=
∫ (2)
The RMS delay spread is the square root of the second central
moment of a power-delay profile. It is the standard deviation about
the mean excess delay, and is expressed as:
( )1/ 22 ( )RMS e A P dτ τ τ τ τ τ⎡ ⎤= − −⎢ ⎥⎣ ⎦∫ (3)
Where Aτ is the first-arrival delay, a time delay corresponding
to the arrival of the first transmitted signal at the receiver; and
eτ is the mean excess delay, the first moment of the power-delay
profile with respect to the first arrival delay:
( ) ( )e A P dτ τ τ τ τ= −∫ (4) The RMS delay spread is a good
measure of the multipath spread. It gives an
indication of the nature of the inter-symbol interference (ISI).
Strong echoes (rela-tive to the shortest path) with long delays
contribute significantly to RMSτ .
A typical plot of the time delay parameters is shown in Fig.
3.
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6
– Analysis of Results In this section, an analysis of the
measured results, estimation of coherence
bandwidth, its variability and interrelationship with RMS delay
spread are out-lined.
Coherence Bandwidth Results Fig. 4 shows the frequency
correlation functions obtained for three transmitter
receiver scenarios; a class 9 channel (curve (i)), which can be
assumed to have the least multipath contributions. Curves (ii) and
(iii) correspond to the FCFs obtained from a class 6 and class 3
channels, respectively.
Fig. 3. An illustration of a typical power-delay profile and the
definition of the delay parameters
Fig. 4. Frequency correlation functions of the measured
channels.
(i) class 9; (ii) class 6; (iii) class 3
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The degradation of the frequency correlation functions
corresponding to class 6
and class 3 channels with respect to the class 9 channel can be
seen in Fig. 4. Rapid decrease of the frequency correlation
function with respect to the frequency separation and also as the
class number decreases can be observed. The decrease in frequency
correlation function is not monotonic, and this is due to the
presence of multipath echoes in the PLC channel.
Coherence bandwidth values for 0.5, 0.7 and 0.9 correlation
levels for the curves of Fig. 4 are given in Table 2, and
statistics of the coherence bandwidth function for 0.5, 0.7 and 0.9
correlation levels for all channel measurements are shown in Table
3. In general, the smallest frequency separation value is normally
chosen to estimate the coherence bandwidth.
For the 0.9 coherence level, the coherence bandwidth was
observed to have a mean of 291.97 KHz, minimum coherence bandwidth
of 32.5 KHz, and 334.36 KHz standard deviation (Std). For 90% of
the time, the value of B0.9 obtained was below 691.5 KHz and above
65.5 KHz. For the 0.7 coherence level, a mean co-herence bandwidth
of 833.9 KHz was obtained. Here, the minimum value emerged as 98.5
KHz and the standard deviation as 1.06 MHz. In the 0.5 coher-ence
level, 80% of the channel measurements have a B0.5 values below
13.376 MHz and above 423.5 KHz.
TABLE 2
COHERENCE BANDWIDTH VALUES FOR 0.5, 0.7 AND 0.9 CORRELATION
LEVEL FOR THE CURVES OF FIG. 4.
Curve Coherence bandwidth KHz
B0.5 B0.7 B0.9 (i) 18 819.5 3 852.5 1 586.5 (ii) 2 171.5 586.5
249.5 (iii) 909.5 347.5 50.5
TABLE 3
STATISTICS OF THE COHERENCE BANDWIDTH FUNCTION FOR 0.5, 0.7, AND
0.9 CORRELATION LEVELS
M
in Max
Mean
Std 9
0% above
90% be-low
B0.5 (KHz)
230
33 850.5
4 539.3
6 544.7
423.5
13 376
B0.7 (KHz)
98.5
8 054.5
833.9
1 063.2
181.5
1 774.5
B0.9 (KHz)
32.5
1 859.5
291.97
334.36
65.5
691.5
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Coherence Bandwidth versus Channel Class The min, max, and mean
values of coherence bandwidth function for 0.9 corre-
lation level as a function of the channel class is given in Fig.
5. It can be observed that the coherence bandwidth is highly
variable with the location of the receiver with respect to the
transmitter.
Fig. 5. Coherence bandwidth for 0.9 correlation level as a
function of channel class. (i) Min; (ii)
Mean; (iii) Max To investigate the reasons for the fluctuations
of the values of coherence band-
width, magnitude curves of the complex frequency responses are
shown. Fig. 6 represents the channel frequency response for the
case where the coherence band-width was estimated at 1.859 MHz.
This is the dominant peak value that appears in the curve (iii) of
Fig. 5. Fig. 6 clearly shows that the channel frequency re-sponse
presents few notches, large peaks, and is relatively flat over the
100 MHz bandwidth. Not surprisingly therefore, the coherence
bandwidth assumed a rela-tively high value.
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9
Fig. 6. Measured transfer function envelope of the maximum B0.9
value
Next, the least value of the coherence bandwidth (32.5 KHz) was
investigated.
Fig. 7 shows the magnitude response in this case which shows
significant fre-quency selective fading of the channel, resulting
in deep fades at several frequen-cies and narrow peaks. The
presence of this significant frequency selective fading explains
the relatively small value of coherence bandwidth observed. Both of
these cases demonstrate that the PLC indoor channel is considerably
affected by multipath, and that the coherence bandwidth value
decreases with frequency selec-tive fading.
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Fig. 7. Measured transfer function envelope of the minimum B0.9
value From an implementation point of view, the highly fluctuating
coherence band-
width means that the system designer can rely only on the lowest
value of this pa-rameter in such an environment. From Fig. 5, this
is 32.5 KHz.
The coherence bandwidth, determined from (1) is calculated from
the complex frequency response of the channel, in which the phase
changes instantaneously and significantly over any change on the
state of an electrical device. The coher-ence bandwidth thus
determined is more appropriately termed the instantaneous coherence
bandwidth. To study the time dispersive nature of the PLC channel,
it's more suitable to focus on the RMS delay spread parameter.
Delay Spread Results By means of an inverse Fourier transform
the impulsive response ( )h t can be de-
rived from absolute value and phase of a measured transfer
function. The ampli-tudes of the impulse responses of the channels
of Fig. 6 and Fig. 7 are depicted in Fig. 8 and Fig. 9,
respectively.
Fig. 8. Impulse response of the channel of Fig. 6.
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Fig. 9. Impulse response of the channel of Fig. 7.
The impulse responses of Fig. 8 and Fig. 9 show some peaks which
confirm the
multipath characteristics of PLC channels. The impulse response
of Fig. 8 exhibits a maximum peak at a delay 0.01A sτ μ= and an RMS
delay spread 0.0368RMS sτ μ= . The same parameters of the impulse
response of Fig. 9 are 0.32A sτ μ= and 1.3674RMS sτ μ= . This is
quite foreseeable as the impulse re-sponse of Fig. 8 is associated
to a shorter PLC channel and much less affected by multipath.
Statistics of First arrival delay and RMS delay spread for all
measured PLC channels are given in Table 4. The first-arrival delay
( Aτ ) was observed to have a mean of 0.175μs, minimum of 0.01μs,
and 0.11μs standard deviation. 80 % of the channels exhibit an RMS
delay spread between 0.06μs and 0.78μs. The mean value of the RMS
delay spread was 0.413μs.
TABLE 4 STATISTICS OF TIME-DELAY SPREAD PARAMETERS
Min Ma
x Me
an Std
90%
above
90% be-low
( )A sτ μ
0.01
0.55
0.1751
0.1134
0.05
0.31
(RMS sτ μ
0.027
1.367
0.413
0.294
0.066
0.784
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Delay spread versus Channel Class The mean values of
first-arrival delay and RMS-delay spread as a function of the
channel class are given in Fig. 10. It can be observed that
these parameters are highly variable with the class number.
Fig. 10. Time-delay spread parameters as a function of the
channel class
Generally speaking, the first arrival delay and RMS delay spread
parameters de-
crease with the class number. In fact, the highly numbered
classes are those whose channels are shorter and less affected by
multipath. The transmitted signal arrives to its destination more
quickly; furthermore, the number of echoes and their delay excess
are less than those of low numbered classes.
An important fact is that the average value of the RMS delay
spread of the class 4 channels is higher than that of classes 2 and
3. Indeed, the relatively small num-ber of measurements made that
class 4 channels, although with higher average magnitude than those
of the classes 2 and 3 channels, have many low valued cohe-rence
bandwidth channels (the B0.9 32.5KHz min value pertains to the
class 4) and thus many RMS delay spread values relatively
large.
Coherence Bandwidth versus RMS Delay Spread Fig. 11 shows a
scatter plot of the RMS delay spread against the coherence
bandwidth of the PLC channel measures. The scatter plot shows a
high concentra-tion of points in the range 0.1μs-0.9μs at which the
coherence bandwidth is almost under 500 KHz and over 50 KHz. Higher
values of coherence bandwidth are ob-served for RMS delay spread
values less than 0.1μs. In system design terms, higher coherence
bandwidth translates to faster symbol transmission rates [10].
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Fig. 11. Scatter plot of coherence bandwidth against RMS delay
spread.
Fig. 11 depicts a clear relation between the values of B0.9 and
RMSτ estimated in
the overall set of measured channels, and which can be
approximated by:
0.9
55( )( )RMS
sB KHz
τ μ = (5)
On Fig. 11, the relation (5) is represented by the red circles
curve.
– Conclusion Based on a multitude of measurements in different
environments, the paper in-
cludes analysis of both coherence bandwidth and RMS delay spread
parameters for in-house powerline channels in the frequency range
up to 100 MHz.
Rapid decrease of the frequency correlation function with
respect to frequency separation and also as the channel class
increases was observed.
The 90th percentile of the estimated coherence bandwidth B0.9 at
0.9 correlation level stayed above 65.5 KHz. Also, 90% of estimated
values of B0.9 were below 691.5 KHz. B0.9 was observed to have a
minimum value of 32.5 KHz.
The RMS delay spread results show that 80 % of the channels
exhibit values between 0.06μs and 0.78μs. Its mean value was equal
to 0.413μs.
Additionally, a relationship between the RMS delay spread and
the coherence bandwidth was determined.
These results are intended for applications in high-capacity
indoor powerline networks whose frequency band is up to 100MHz.
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14
REFERENCES [1] Homeplag Powerline Alliance, "HomePlug AV
Specification, Version 1.0.05", October 2006. [2] Sherman Gavette,
Sharp Labs, "HomePlugAV – Detailed Architecture", homeplug
executive
seminar, November 2005. [3] Bultitude R., Mahmoud S., and
Sullivan W., "A comparison of indoor radio propagation charac-
teristics at 910MHz and 1.75 GHz", IEEE J. Sel. Areus Commun.,
January 1989, 7, (l), pp. 20-30.
[4] Bultitude R., Hahn R., and Davies R., "Propagation
considerations for the design of indoor broadband communications
system at EHF", IEEE Trans. Veh. Technol., February IYY8,47, (I), ,
pp. 20-30.
[5] V. Degardin, M. Lienard, A. Zeddam, F. Gauthier, and P.
Degauque, “Classification and charac-terization of impulsive noise
on indoor power lines used for data communications”. IEEE
Trans-actions on Consumer Electronics, Vol. 48, November 2002.
[6] T. Esmailian, F. R. Kschischang, and P. Glenn Gulak,
“In-building power lines as high-speed communication channels:
channel characterization and a test channel ensemble”, Int. J.
Comm. Sys. 2003.
[7] T. V. Prasad, S. Srikanth, C. N. Krishnan, and P. V.
Ramakrishna, “Wideband Characterization of Low Voltage outdoor
Powerline Communication Channels in India”, International Symposium
on Power-Line Communications and its Applications (ISPLC’2001),
Sweden, April 2001.
[8] Holger Philipps, "Development of a Statistical Model for
Powerline Communication Channels", Proceedings of ISPLC 2000,
pp.153-162
[9] M. Tlich, A. Zeddam, F. Moulin, F. Gauthier, and G. Avril, "
A Broadband Powerline Channel Generator", Proceedings of ISPLC
2007, pp. 505-510, 26-28 March 2007.
[10] Lutz H.-J. Lampe and Johannes B. Huber, "Bandwidth
Efficient Power Line Communications Based on OFDM"